Obtaining unknown mean and variance using standardization
Obtaining unknown mean and variance using standardization
IB Year 6 | Grade 12
A certain product is put into cans by a canning machine. The mass of product in a can is normally distributed with mean \(m\) and standard deviation \(0.5\) g. The value \(m\) can be adjusted by the operation of the machine. The cans are labelled as containing at least \(300\) g of product, and the operator wishes to set the mean so that not more than \(2\) can in \(1000\) on average will contain less than \(300\) g of product. Find the least value of \(m\) which will enable this to be achieved.
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Answer:\(m_{\min}=300-0.5\Phi^{-1}(0.002)=301.4390808695\ldots\text{ g}\). If settings use \(0.001\text{ g}\) increments, the least feasible setting is \(301.440\text{ g}\).
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